A very powerful Panorama programme on Monday night has turned the focus back to the prospect of the UK's population reaching 70 million in 20 years' time, followed by substantial further growth. Whether or not this projection is credible lies at the very heart of the immigration debate.

These projections are produced by the government's own statisticians in the Office for National Statistics (ONS), now under the aegis of the newly independent UK Statistics Authority. Obviously such projections become more uncertain the further ahead one looks. The government makes hay with a 1960s projection for the following 40 years which, by 2000, was spectacularly wrong. Back then the ONS assumed that the baby boom would continue – and it didn't.

Their record has greatly improved in the half century since then. Indeed, at the 20-year range which we are now discussing they have been accurate to within 2.5%. But could they yet be wrong?

It is important to be clear that there are only three variables – deaths, births and net migration. The mass migration of recent years has made immigration by far the largest factor – accounting for just over two thirds of the population increase projected for the next 20 years. That is why we can usefully consider a broad population policy without descending into absurdities like emulating China.

It is equally important to be clear that projections are not forecasts. By their nature, they take no account of future changes in government policy and only limited account of economic developments. They are, essentially, a construct based on assumptions about birth, death and immigration but they do show what is very likely to happen unless very firm measures are taken. And the existing age-structure gives the projections some stability: all the mothers for the next two decades have already been born, bar immigration. The question therefore resolves into whether these assumptions are convincing.

The simplest is the death rate. Life expectancy has increased steadily since the 1970s but the ONS principal projection conservatively assumes a lower rate of improvement in survival after 2033, down to 1% a year.

The birth rate fluctuated hugely between 1945 and 1975 but since then has varied within a much narrower band. The most commonly used measure is the total fertility rate (TFR), which shows the average number of children per woman if fertility patterns continue as at present. The TFR in 2008 was 1.95 (just below the 2.06 replacement rate) but the ONS took a more conservative assumption of 1.84 for their latest principal projection.

The major factor – net immigration – is rather more difficult. It reached a peak of 245,000 in 2004, declining to 163,000 in 2008. The ONS has assumed that it will continue into the future at 180,000. The government argues that immigration has fallen and implies that it will continue to fall, partly as a result of their points based system. The main reason for the fall in 2008 was a sharp reduction in net migration from eastern Europe, which accounted for 95% of the drop (and, of course, had little or nothing to do with government policy). The ONS has taken this into account and expects net migration from eastern Europe to fall to zero in five or six years' time. They have also tried to iron out fluctuations by looking at net migration over three-year periods. As for economic factors, the record shows that immigration falls in each recession but then resumes its strong upward trend.

What is inescapable is that immigration would have to fall very substantially to avoid the projected growth in population. Without any immigration at all, population would increase to 65 million on the birth and death rates assumed by ONS. Net immigration would have to fall to 50,000 a year – a quarter of the level of recent years, and less than one third of the ONS assumption, to prevent the UK population reaching 70 million. How is that going to happen, without a radical change of immigration policy?

That brings us to the crux of the argument. Britain is already, with Holland, the most crowded country in Europe. Most immigrants go to London and the south-east. Schemes to oblige them to work and remain in places less attractive to immigrants are unrealistic and unenforceable. There is a strong case to be made that the quality of life and social cohesion of our society as a whole will be severely affected by continued population growth on anything like the current scale.

The view of the public is very clear. According to the latest Sunday Times, 74% think immigration into the UK is too high and the government's own survey, conducted by the Department for Communities and Local Government in February 2010, found that 77% want to see immigration reduced and 50% want it reduced "by a lot". Of the ethnic respondents, 25% also wished to see immigration reduced by a lot.

Faced with such a clear expression of public opinion, repeated in poll after poll, and with the practical consequences of mass immigration highlighted in the Panorama programme, it is surely the government's duty to take firm measures on immigration policy to ensure that the population increase now projected does not take place. Instead, they seem to be in a state of denial.